Description Usage Arguments Details Value References See Also Examples

Compute Principal-component-based Khattree-Bahuguna's Multivariate Skewness.

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`x` |
a matrix of original scale observations. |

`cor` |
a logical value indicating whether the calculation should use the correlation matrix ( |

Let *\mathbf{X} = X_1, …, X_p* be a *p*-dimensional multivariate random vector. We compute the sample skewness for *p* principal components of *\mathbf{X}* respectively by the sample Khattree-Bahuguna's univariate skewness formula (see details of `kbSkew`

that follows). Let *η_1, η_2, …, η_p* be the *p* univariate skewnesses for *p* principal components. Principal-component-based Khattree-Bahuguna's multivariate skewness for a sample is then defined as

*η = ∑_{i=1}^{p} η_i.*

Clearly, *0 ≤ η ≤ \frac{p}{2}*.

`pcKbSkew`

gives the sample principal-component-based Khattree-Bahuguna's multivairate skewness.

Khattree, R. and Bahuguna, M. (2019). An alternative data analytic approach to measure the univariate and multivariate skewness. *International Journal of Data Science and Analytics*, Vol. 7, No. 1, 1-16.

`kbSkew`

for Khattree-Bahuguna's univariate skewness.

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